"Upward, Not Northward":
Flatland and the Quest for the New
ELLIOT L. GILBERT
University of California, Davis
When perceptible amounts of new phenomenal being come to birth, must we hold
them to be in all points predetermined and necessary outgrowths of the being already
there, or shall we rather admit the possibility that originality may thus instill itself
into reality?
William James, Some Problems of Philosophy^
"Your country of two dimensions is not spacious enough to represent me, a [Sphere]
of three, but can only exhibit a slice or section of me, which is what you call a Circle.
. . . You cannot indeed see more than one of my sections, or Circles, at a time, for you
that as I rise in space my sections become smaller. See now, I will rise; and the effect
upon your eye will be that my Circle will become smaller and smaller till it dwindles
to a point and finally vanishes."
Edwin A. Abbott, Flatland
Kaluza showed that electromagnetism is actually a form of gravity, but not the
What [he] was saying in his bold conjecture was that if we enlarge our vision of the
that electromagnetism is only that part of the gravitational field which operates in
the extra dimension of space we have failed to recognize. . . What he did provides
a classic example of creative imagination.
Paul Davies, Superforce^
IN 1980, THE ARION PRESS of San Francisco published a limited
edition of Edwin A. Abbott's "romance of many dimensions," Flatland,
printing the text on heavy, hand-laid paper in a single fan-fold gathering
and providing for each copy elaborately machined aluminum covers and
an equally formidable aluminum slipcase. This metallic sheathing of the
volume argues, as the publisher no doubt intended it should, for the
extraordinary value of the bibliographical objet—the fine paper and
beautiful printing—^being so dramatically guarded. But it also, though
perhaps less consciously, seems to assert the value of the text itself.
ELT:
VOLUME 34:4,
1991
suggesting that Flatland, as a cultural artifact of unusual importance,
must be carefully protected and preserved.
For the purely literary survival of the Flatland text no such heroic
precautions are necessary. The slim book by schoolmaster and Church of
England cleric Abbott, first published more than a century ago, has since
run through twenty-five editions, a number of which are even now in
print; thus, the work hardly needs to be rescued from neglect or oblivion.^
What may be in some need of protection and preservation, however, is
the thematic significance of this perennially charming story, part sciencefiction adventure, part Socratic dialogue, a significance that appears to
have struck even the earliest readers as mysterious. "The book seems to
have a purpose,' wrote an 1884 reviewer in the Athenaeum, "but what
that may be is hard to discover,'"* a judgment the New York Times
seconded the following year when it described the first American edition
of Flatland as "a very puzzling book."^ And nearly a hundred years later,
Ray Bradbury, in his introduction to the Arion edition, suggests that
Flatland continues to challenge interpretation, declaring that "Abbott
pretends to be doing one thing, but is truly doing another.'"'
So many readers over so long a period have surely not been wrong
to sense in Abbott's provocative little book some unstated thesis, and it
will be my own thesis here that in Flatland we are dealing with an
unassuming but insightftol study of a persistent nineteenth-century
preoccupation, the quest for new creative directions in a culture
powerfully—if more and more uncomfortably—committed to history and
tradition. In seeking sources for that new creativity, Abbott turns for
help first to tradition and then to the individual but finds them both
inadequate to the challenge, each capable only of reiterating what has
already been done, what already exists. By the end of the book, therefore,
he is left to posttilate an as yet unidentifiable third direction or third
dimension from which, if any vita nuova is in fact possible, such an
innovation must come.
As to what, in Bradbury's words, Abbott "'pretends to be doing" in
Flatland—what, that is, he overtly sets out to accomplish—that seems
clear enough; he undertakes to "'edit" the memoir of an inhabitant of a
two-dimensional universe who records the consequences of a visit he has
received from a three-dimensional intruder. The two-dimensional
memoirist's struggle with the concept of a third dimension gives Abbott
an opportunity to discuss the analogous problems his own three-
GILBERT: QubaT FOR THE NKW
dimensional readers have with the concept of a fourth dimension, and as
one recent commentator has put it in a testimonial to the author's
success, the events and illustrations in Flatland offer "the clearest
imagery of the fourth dimension to which [most non-experts] are likely
to attain."'
The nature of this success of Abhott's should he clearly understood.
The editor of a recent edition oiFlatland tries to work up a kind of hogus
astonishment in his readers at the prescience of Abhott's achievement by
pointing out that when Flatland was written "Einstein was a mere
child."® But the critic then goes on to concede that Abbott was writing
during years when the abstract concept of multi-dimensionality was quite
well known among mathematicians and physicists; just the moment, that
is, when the lay public wotild have been ready for some dramatic and
picturesque explanation of so intriguing an idea.^ And to offer such an
explanation there could have been no one more appropriate than Abbott,
who, as headmaster for more than thirty years of the City of London
School, the most progressive boys' school of its day, and as the author of
nearly fifty books on a wide variety of subjects, had devoted his life to
making abstruse knowledge intelligible to non-specialist audiences.
The titles alone of some of these books suggest their pedagogical
intention: How to Write Clearly, English Lessons for English People,
Shakespearian Grammar, designated on the title page as "for the use of
schools," and Clue: A Guide Through Greek to Hebrew Scriptures. This
last in particular demonstrates both Abbott's ambition and his skill as
a popularizer of diffictilt subject matter, being no less than a treatise on
the Greek, Hebrew, and Aramaic sources and translations of the Bible,
written—in Abbott's words—"to be made clear to the simplest intelligence. Even of the details a large number can be mastered without
knowledge of any ancient language."^" Other of Abbott's books, especially
Through Nature to Christ and The Kernel and the Husk, seek to cast
light on the contemporary debate over the proper role of imagination in
scientific theory, while still others, notably Philochristus, Memoirs of a
Disciple of the Lord, Onesimus, Memoirs of a Disciple of St. Paul, and
Silanus, the Christian, take on the task of clarifying biblical themes as
well as language." These last three works, all best-selling historical
romances, stress, in a Carlyleian spirit, the inescapable "presentness'' of
the past as well as offering the kind of imaginative, circumstantial
recreation of an exotic culture that also makes Flatland so appealing.
ELT: VOLUMK 34:4, 1991
Despite their great variety of subject matter, however, Abbott's
books tend to return again and again to a few principal ideas, all of
which, as we shall see, receive their most memorable expression in
Flatland. In the historical romances, for example, particularly
Philochristus, Abbott focuses on a favorite subject, represented by the
struggle between the Scribes of Galilee, who try to teach the protagonist
"not to trust the voice within [him], namely [his] conscience, but only to
tradition and authority,"'"^ and Jesus, who speaks "not according to rule,
nor out of any books or traditions, but as it were out of himself."" On the
whole, in the familiar conflict between historical authority and personal
inspiration—between tradition and self—as sources of knowledge, Abbott
tends to prefer the interior to the exterior voice, new knowledge to old.
But he is also aware of the dangers of an indiscriminate self-reflexiveness, and in his biography of Francis Bacon he quotes with approval
Bacon's warning against solipsistically "impress[ing] the stamp of our
own image on the creatures and works of God instead of carefully
examining and recognizing in them the stamp of the Creator himself.""
Abbott even goes so far, in Silanus, the Christian, as to assert that it is
"much better (and less misleading) to remain in the old-fashioned belief
that a good and wise God created the world in six days than to adopt a
new belief that a bad or unwise or careless God—or a chance, or a force,
or a power—evolved it in sixty times six sextillions of centuries."^^
Clearly, the ambivalence Abbott felt about this epistemological problem
ran deep, perhaps deeper than he knew, though he openly acknowledges
the paradox in the introduction he wrote for his father's Alexander Pope
concordance, praising the poet on the one hand for his refusal to pursue
novelty and on the other for his pioneering of modern English.^®
The championing of modern English, and in particular the
promotion of an English vernacular over a classical patrius sermo, is
another of the forms Abbott's preference for the present over the
past—the new over the old—characteristically takes in his works. In
Shakespearian Grammar, for example, the writer speaks up for the
teaching of English language and literature in the schools, arguing—
modestly enough, to be sure—that "it is a positive gain to classical
studies to deduct from them an hour or two every week for the study of
English."" But he could be much livelier in his advocacy of the vernacular, vigorously attacking Bacon, for instance, for identifying Latin with
the authoritative historical record and for considering English ephemeral.
incapable of reaching and shaping the future. Of the Latin translation of
his own Advancement of Learning Bacon had declared, "It is a book, I
think, will live, and be a citizen of the world, as English books are not."'®
Abbott takes considerable—if rather unclerical—pleasure in pointing out
how wrong Bacon was.
Ironically, for all the many ambitious, serious-minded works Abbott
composed to promote his ideas about these issues of authority, inspiration, creativity, and faith, only the little jeu d'esprit of a volume he
called Flatland, published pseudonymously in 1884, is still read today
and has itself lived to be a citizen of the world. It is, of course, easy to
understand why the book should continue to attract modern readers for
whom the theological conflicts and linguistic skirmishes of the past no
longer hold any interest. Speculation about unknown dimensions will
always be appealing, and it was surely a stroke of genius for Abbott to
populate his mathematical allegory with living geometrical figures—the
two-dimensional protagonist is a Square, his three-dimensional visitor a
Sphere—lending the story a timeless fairy tale charm. The verisimilitude
provided by the Square's solemn efforts to describe the anatomy of
Flatlanders and the structure of their social and political systems only
adds to that charm. And then, the cultural issues—class warfare, for
example, or the condition of women—that Abbott depicts as challenging
the book's exotic inhabitants continue, with remarkably few changes in
teiTns and form, to confront us today.
Though these larger cultural implications of the story ought to have
been clear enough to the work's original audience, the puzzlement of the
first reviewers, their sense that something besides a discussion of
dimensionality, something they couldn't quite grasp, was going on in the
book, suggests that from the start Flatland seemed enigmatic. Perhaps
the absence of its author's name from the title page was disorienting,
depriving readers of the conventional expectations a book acknowledged
to be by Abbott might have raised. And indeed there is a sense in which
Flatland really is an anonymous work. In all his other books Abbott
speaks to us authoritatively—as it were in his own name—on subjects
about which he is, and is recognized to be, an expert. In Flatland, on the
other hand, though the discussion of dimensionalty requires some small
expertise, the voice we hear is very much that of a non-specialist
literally an ordinary citizen of Flatland, a Square moyen sensuel who
describes the details of his culture without comment or self-consciousness
ELT:
VOLUME 34:4,
1991
and without any apparent intention to instruct, except in mathematical
matters. Naturally, in assembling those cultural details Abbott would
have drawn upon his own social, political, and philosophical interests,
but as the contemporary success of so many of his other books suggests,
those interests closely paralleled the concerns of the society as a whole.
Curiously, then, Flatland, for all its quirky geometric fantasy, is also a
book to which we can turn today, more confidently than to many more
serious historical studies, for an accurate representation of nineteenthcentury life and thought.
The book is, indeed, almost an index to the intellectual, spiritual,
and artistic preoccupations of the period. One early reviewer finds in the
work, for example, "an effective satire on social differences,"'^ and such
differences do in fact play a significant role in the story. As Abbott
describes it, Flatland society is a rigorously hierarchical one with a
structure that appears to be firmly rooted in the curious physiology of its
members. The marks of Flatland aristocracy are regularity and manysidedness. All but the lowest orders of the culture (and women) are
regular polygons, the equilateral triangles (or middle class) representing
the first stage of respectability, squares, pentagons, and higher polygons
(or gentlemen and nobles) intermediate levels, and the circles—actually
figures with so many sides that they approach true curvature without in
fact achieving it—the final or priestly stage. Below the equilaterals is the
great swarm of irregular triangles (what the narrating Square refers to,
with no apparent sense of impropriety, as "the wretched rabble of the
Isosceles"), whose sharp angles constitute a life-threatening danger to the
more cultivated, obtuse-angled polygons and who are consequently despised and shunned, though employed as expendable workers, soldiers,
and guards. So absolutely is the social structure of Flatland determined
by the physical distinctions among its inhabitants that though over the
centuries there have been no fewer than 120 rebellions and 235 minor
outbreaks instigated by the Isosceles, every one of these violent attempts
to reorganize the culture has failed.
The satire here of an essentialist British class system in the late
nineteenth century is clear enough, and the scope of that satire is soon
extended through a consideration of Flatland genetics. As we are informed by the Square, the laws of generation for regular polygons in the
society decree that every son shall have one more side than his father,
an amusing glance, we may suppose, not just at aristocratic pretensions
GILBERT: QUEST FOR THK N E W
but at a more general Victorian faith in progress.^" Abbott has, however,
a further and subtler point to make here, developing the idea that because progress, defined in such a mechanical way as this, is entirely
predictable, it is necessarily sterile and without hope of creativity, only
demonstrating the futility of mere accumulation as a means of achieving
the new, just as the repeated failures of the Isosceles's rebellions
demonstrate the futility of attempting, by conventional means, to change
the traditional political structures of Flatland society. The theme is, as
I have said, one the author deals with frequently in his other works, and
it grows in importance in Flatland as the story proceeds.
Another approach to this theme is provided by the culture's virulent
misogyny, from the outset one of the book's most conspicuous and
controversial features. Not surprisingly, several of the first reviewers
singled this element of the story out for special comment, most remarking on its satiric intent. The generally hostile New York Times critic, for
example, concluded that what "little sense" the book appeared to make
lay in its "appeal for the education of women,"^^ while the more supportive commentator for the Boston Advertiser applauded "the good
natured mockery and absurd extravagance"^^ evident in Flatland's denigration of the female. But some early readers apparently mistook
Abbott's straight-faced portrayal of that denigration for acquiescence, if
not approval, since the preface to the second edition of the work was felt
to require a defense of the book's author—ostensibly the Square—against
charges of being "a woman-hater.'' And such a judgment of the author's
attitude toward women in the story seems still to be possible. In the
introduction to the 1980 Arion Press edition of Flatland, for example,
Ray Bradbury speaks of the "amusing and perhaps irritating attitudes
on women'' in the work but makes it clear that he is not among those
irritated. Indeed, he accepts as both seriously intended and reasonable
the book's assertion that intellectual and emotional distinctions between
men and women, like the physical distinctions between Isosceles and
Regular Polygons, are irremediable, simple facts of life that have not
changed substantially in the century since Abbott first published
Flatland and that are unlikely to change in the next hundred years.
In a way, such a variety of readings testifies to the skill with which
Abbott has entered into the unreflecting mind of his protagonist to
present the condition of women in Flatland. Because (we learn from the
Square) Flatland females, regardless of their pedigree or social position.
are all born straight lines, they are more dangerous, and inevitably rank
lower in the esteem of the culture, than the sharpest angled of Isosceles
males. With the merest touch of their pointed bodies meaning death
("What can it be to run against a Woman, except absolute and immediate
destruction"'''), these femmes faiales must be rigorously controlled by
society, which obliges them, as safety precautions, to render themselves
conspicuous by keeping their hindquarters always in motion (Abbott's
wry comment, we may assume, on an exaggerated—and threatening—
female sexuality), and to warn others of their approach by continually
chanting what is called a "peace song." Then, because they lack any
angle at all, Flatland ladies are virtually without brains and so receive
no mental education, a fact that, according to the Square, burdens males
with the necessity of leading
a kind of bilingual, and I may almost say bi-mental, existence. With Women,
we speak of "love," "duty," "right," "wrong," "pity," "hope,' and other irrational
and emotional concepts, which have no existence, and the fiction of which has
no object except to control feminine exuberances; but among ourselves, and in
our books, we have an entirely different vocabulary and I may almost say,
idiom. "Love"' then becomes "the anticipation of benefits"; "duty"' becomes
"necessity" or "fitness"; and other words are correspondingly transmuted.^'*
Whether we view this as a satire on Victorian over-protection of
women, a sardonic version of Abbott's usual interest in the relationship
between the patrius sermo and the vernacular, or a remarkable prefiguring of the concept of phallogocentrism,"^ we can certainly understand
how, for the Times reviewer, Flatland might have appeared to be appealing for a change in the system of education for women. But behind such
a hopeful appeal we, along with Bradbury, can also see Abbott defining,
as he had done before in his discussion of the culture's class system, a
condition seemingly so rooted in anatomical reality, so deeply entrenched
in what might be described as the history of the germplasm, that no
imaginable social or political reform can begin to resolve it; that under
such circumstances no true creativity is possible.
What is perhaps the story's most powerful single episode makes a
similar point. During an historical period of unrest called the "Chromatic
Sedition,'' a group of despised mutants or "irregulars,'' allying themselves
with the culture's dissident females, had sought to change the structure
of Flatland society so radically that, among other things, there would no
longer have been any practical way of distinguishing between women and
398
GILBERT: Q U I B T FOR THE N E W
priests. Abbott's parody here of both the woman's suffrage movement and
fin de siecle aestheticism and decadence, together with his recognition of
the hnk between these two major revolutionary forces of his own day,
appears at first to suggest that change, that a new direction, is not
impossible even in a society as rigid as Flatland's. But in the end
anatomy proves to be destiny after all as the insurgent women discover
that, given the physical limitations of their bodies and their world, they
will be worse off under the proposed new freedom than under their traditional constraints. With this, they turn on their deviant allies and
eagerly participate in their destruction, demonstrating once again that
a desire for the new must be extraordinary indeed that can overcome
genetic and geometric necessity.
One creative response to a culture like Flatland's, so inflexibly
structured by tradition and anatomy as to suppress all individual
initiative and render any movement in a new direction impossible, would
be, we might suppose, a powerful assertion of self, some ringing
announcement of personal sovereignty. But as Abbott goes on to
illustrate in his story, such self-assertion, leading inevitably to solipsistic
self-delusion, is equally futile as an instrument of creativity. In one of
the book's most striking episodes, the Square has a dream in which he
is conducted by the Sphere on a visit to Pointland, an anomalous world
inhabited by a single creature whose own being constitutes its entire
universe. This "king" of what the Sphere calls "the abyss of No dimensions" leads a life of narcissistic contentment, continually singing his own
praises in grammatically ambiguous language that makes no distinction
between self and other: "Infinite beatitude of existence! It is; and there
is none else beside It," the tiny monarch soliloquizes, addressing himself
in the third person as the Square and the Sphere look on contemptuously "It fills all space, and what It fills. It is. What It thinks, that It
utters; and what It utters, that It hears; and It Itself is Thinker, Utterer,
Hearer.
It is the One; and yet the All in All. Ah, the happiness of
Being!"^''
Disgusted at the complacency of this puny, no-dimensional creature,
trapped in what Walter Pater had already famously described as the prison of the mind, the Square tries, with a stern lecture, to shock the little
king into a knowledge of his own limitations, into an awareness of the
existence of others in the universe. But as the Sphere has predicted,
decrying the solipsism of "people who cannot distinguish themselves from
the world,' the tiny monarch easily assimilates the intrusive voice into
his own private vision by assuming it comes from himself. "Ah, the joy,
ah, the joy of Thought!" he chirps still more enthusiastically, his selfjustification slyly mimicking the Miltonic God or perhaps even the
Whitmanic ego: "What can It not achieve by thinking! Its own Thought
coming to Itself, suggestive of Its disparagement, thereby to enhance Its
happiness! Sweet rebellion, stirred up to result in triumph! Ah, the
divine creative power of the All in One!""
Creative power, however, is precisely what the king of Pointland
lacks, as Abbott is at pains to make clear. For where the only source of
knowledge is the self, as in the king's case, one soon exhausts the forms
and ideas implicit in that knowledge and permitted by the configuration
of that self, and then there is nowhere to turn for new forms and ideas.
But how, then, we are left to wonder by the structure of Abbott's
argument thus far, can creativity ever be achieved? If history, genealogy,
and tradition on the one hand, and solipsistic self-absorption on the
other, equally limit life to the established and predictable, to a recapitulation of what has already occurred, where exactly is the new to come
from? The logical answer would seem to be that it must come from some
source that is neither tradition nor self; and indeed it is to the identification of such a third source that Flatland devotes itself most energetically
and originally, the book's nominal search for a third dimension in a twodimensional world—for a new spatial direction—neatly fusing mathematical and metaphysical quests.
The key event in the story is the apocalyptic arrival of a Sphere, a
solid creature from the universe of three dimensions, in the twodimensional world of Flatland just at midnight on the first day of the
third millenium. The Sphere has come to Flatland to preach what he
calls "the Gospel of the Three Dimensions," a mission he is allowed to
undertake only once every thousand years, and he chooses for his
potential apostle a respectable member of Flatland's professional class,
a Square who, as a student of mathematics, seems a particularly promising candidate for enlightenment. Hovering above the plane surface of the
host world, the visitor announces his presence to the astonished Square,
whose immediate problem is to identify the direction from which the
voice is coming. Because he is a two-dimensional creature existing in a
two-dimensional universe, the Square knows only two directions, those
designated on a map by the east/west and north/south axes. The Sphere,
GILBERT: QUKST FOR
speaking from a third direction, a direction perpendicular to the map-hke
plane of Flatland, is, from the point of view of the Square, who lives
entirely within the surface of that plane, speaking from nowhere.
Not that the Sphere has any trouble making himself visible. This
he easily accomplishes by passing his body downward through the
Flatland plane, an action he is convinced will infallibly demonstrate the
mysterious third direction he has come to reveal. But what to the Sphere
seems so self-evidently a movement perpendicular to the Flatland surface
is perceived very differently by the two-dimensional inhahitant of that
surface. To the Square, who can see only whatever section of the descending Sphere is being cut by the plane at any given moment, his
visitor appears first to be a point, then a small circle, then a series of
increasingly larger circles, then smaller circles again, then a point, and
then nothing.^^ That is, from the perspective of the Square, the Sphere's
movement, consisting, as it appears to do, of the expanding and contracting of a circle, is entirely limited to the two familiar directions that
define the Flatland plane and gives no hint whatever of perpendicularity.
The Sphere decides to try another approach, intending this time to
demonstrate the existence of three-dimensional objects by geometric
analogy with two-dimensional ones. But he soon runs into a problem of
terminology, particularly with the word "upward,' by which he means,
once again, the direction perpendicular to Flatland's surface. To the
Square, however, who, as the Sphere puts it, "has no power to raise his
eye out of the plane of Flatland," "upward" can only mean the direction
designated on a map as "Northward," and he says so. To which the exasperated Sphere replies, "No, not Northward; upward; out of Flatland
altogether," and suiting action to words draws the terrified Square up
into the space above the Flatland plane, up out of his universe's familiar
two dimensions into an unimaginable third.
It is tempting to see in all this a charming if pointed religious
allegory of the sort we might reasonably expect from the author of
Philochristus. There are the more than obvious references to gospels and
apostles and millenia; there is the scene in which the Sphere, in another
effort to illustrate perpendicular motion, gently drops down to touch the
complaining Square's "interior," an amusing enactment of the inward
response, sometimes indistinguishable from dyspepsia, evoked by spiritual enlightenment; there is the traditional martyr's fate of the Square
who, finally convinced of the existence of a third dimension, tries and
ELT:
VOLUME 34:4,
1991
fails to persuade Flatland's priests of its reality, and in the end is imprisoned as a heretic and madman.^^
Ti-oating these elements of the book as religious allegory has the
advantage both of seeing Flatland as something more than social satire
or a clever mathematical primer and of confirming, on still another level,
the intuition of many readers that the work may "'pretend to be doing one
thing, but is truly doing another." In a recent essay, for example,
Rosemary Jann examines the story as, among other things, its author's
"rebuke to the rigid literalism
of fundamentalist religion,' his effort
to create a new alliance between scientific knowledge and religious
faith.^" Still, the religious reading itself limits the scope of the story to
the analysis of a particular kind of creativity, while in Flatland Abbott
appears to be trying to press beyond any specific context toward a
consideration of the creative act in general, toward an examination of the
extraordinary thrust, in a hitherto untried direction, that is required to
accomplish anything really new. And when, in the last page of his
memoir, the unhappy Square records that "in my nightly visions the
mysterious precept, 'Upward, not Northward', haunts me like a souldevouring Sphinx,"^^ he seems clearly to be confirming both the necessity
and the elusiveness of that new direction; acknowledging, with fin de
.siecle apprehension, the unavoidable but ineluctable demands that the
coming century will make on a creativity perhaps unequal to the task.
That the one hope for transcending cultural paralysis should be as
uncertain as it appears to be at the end of Flatland reflects Abbott's
ambivalence about the apocalyptic future which, to the late nineteenth
century, appeared to be approaching so swiftly. Such authorial responsiveness to the spirit of the age is one more reason for valuing this little
book, worthy after all of archival aluminum, as a kind of unintentional
anthology of the period's most persistent concerns. It is remarkable to
note how many of those concerns the author is able to touch on in a brief
hundred pages: the relative merits of tradition and intuition as sources
of knowledge, the burden of history, the appeal of novelty, the deceptiveness of progress, the limitations of hierarchy, the class struggle, the
fear of women (often expressed as the threat of the female), the dangers
of solipsism, the mysteries of creativity.
Of these, this last, properly understood, subsumes all the others. As
Kaluza puts it in my epigraph, "if we enlarge our vision of the universe
to five dimensions there is really only one force field, and that is gravity.''
GILBERT: QUKST FOR THK NEW
In Abbott's own parable of dimensionality, it is the mystery of
creativity—what the book's dedication calls "the enlargement of the
imagination"—that subsumes all those disparate nineteenth-century
philosophical and historical elements catalogued above, elements that
appear fragmented to us only because we lack a sufficiently spacious
vision to see them as aspects of a single cultural "force field.' Historiography, the celebration of self, the emergence of the female, cultural
matters too often studied in isolation from one another, all prove, in their
focus on the overriding issue of the age's search for an elusive vita nuova,
to be—so to speak—different cross-sections of the same sphere.
In Flatland, one way in which fascination with the "mysteries of
creativity' expresses itself is through the quest for a new language to
define the long sought and greatly to be desired new direction. Champion
of a vernacular English during so much of his pedagogical career, Abbott
here identifies creativity with linguistic innovation, and in particular
with a redefinition (which in the end, however, he is unable to supply)
of the word "upward." For the unfortunate Square, imprisoned in the
Pateresque cell of his own experience, there can be only the halfunderstood, visionary knowledge of what "upward" is not, can be only the
conviction, amounting to a religious conversion, that "upward" is no
longer—and can never again be—'"northward." As for what that
unimaginable new direction is, if the equivocal conclusion of Flatland
fails to say, it nevertheless seeks to prepare readers to know it when
they see it: in Abbott's terms, a new dimension, expressed in a new
language, leading to a new life.
Notes
1. William James, Some Profe/ems o/"/*A//o,sop^V
(New York: The Library of America, 1987), 1057, ^
2. Paul Davies, Saperforce, (New York: Simon and
4.
15 November 1884, 622.
5.
23 February 1885.
6.
Ray Bradbury, "Inlroduetion," Flalland (San
every decade since the book's first appearance.
the auLhor of Einsdnn: His Li/e and Times (Now York:
in the U.S.
explanalion. In 1880, fouryearsbefore the appearance
ELT. VOLUME 34;'!, 1991
Hinton published "Wliul. is ihe Fourth Dimension?" in
as Baron Pump\t\glon" The Oxford Thackeray, George
thf Duhlin ilniversily Magazine, addressing hia ossay
Lo
luy
audiouco.
[linlons An
Kpisixlf
A quuitcr
of
i century
of Flcidancl elaborated
later,
on
Saintsbury, ed. (London, 1908), 9: 299.
21.
New York 7Xmes, 2'S Vchruary ISSh.
22.
Boston Atlvertiser, 1885.
number of the goomclric fancies in Abbott's book.
10.
VA\^'\n \ . Mihoil, Clue: A Guide Through Greek
23.
Edwin A. Abbott, Flatland (New York: Dover
Books, 1952), 12.
14. Quoted in Francis Sacon: An Account of His
Life and Works (London: Macmillan, !885), 4 ! 1 . But
nurses—and to learn the vocabulary and idiom of
science' (50).
Like the Square in Flalland, Abbott I
scholars over the original language of the Gospels
Rosemary Jann, "Abbott's Flatland: Scientific
-s (Spring 1985), 478.
Ail^'Tnpt Uj Illustrate
20.
Compare
Sotn€ of th€ Diffcri^nces HatU'ecH
Thackeray's
sardonic
vision
of
aristocratic progress from The Book of Snobs: "Old